Would I write...

While driving east, the forest became denser.

or

As I drove east, the forest became denser.

Also, do I capitalize East?

Both of your sentences are correct.

East is not capitalized in either of these sentences because it means a direction.

I will go with Ms. Sue's answer. It could still be either way around.

.The trees did not do any thing as she moved. The better sentence would be the one using "as"

Both options are grammatically correct, and the choice depends on the context and your writing style.

The phrase "While driving east" suggests that the denser forest is an ongoing event happening at the same time as the action of driving. This phrase emphasizes the simultaneous nature of the two actions.

On the other hand, "As I drove east" suggests a cause-and-effect relationship between the action of driving and the denseness of the forest. This phrase emphasizes that the denser forest is a result of driving east.

Regarding capitalization, while it's not strictly necessary to capitalize "east," it depends on how it is used in the sentence. If it is used as a proper noun to refer to a specific place or region, such as "I drove from the West Coast to the East," then it should be capitalized. However, if it is simply indicating a direction, it does not need to be capitalized, as in "I turned east."

To decide whether to capitalize "East" in your sentence, consider whether you are referring to a specific place or just indicating a direction. If it is part of a larger sentence describing a specific region or location, you should capitalize it. If it is only indicating direction, it does not need to be capitalized.